Resources

Resources

Write a quadratic function from its x-intercepts and another point

f(x)=\sin (x)

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Can we use the intermediate value theorem to say the equation

f(x)=0

has a solution where

\frac{\pi}{6} \leq x \leq \frac{\pi}{3}

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1

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(A) No, since the function is not continuous on that interval.

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0

f\left(\frac{\pi}{6}\right)

f\left(\frac{\pi}{3}\right)

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(C) Yes, both conditions for using the intermediate value theorem have been met.

f(x)=x \cdot 3^{x}

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Can we use the intermediate value theorem to say the equation

f(x)=100

has a solution where

2 \leq x \leq 4

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1

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(A) No, since the function is not continuous on that interval.

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100

f(2)

f(4)

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(C) Yes, both conditions for using the intermediate value theorem have been met.

The graph of a line in the

x y

-plane has a slope of

4

and contains the point

(1,-5)

. The graph of a second line passes through the points

(0,4)

(12,0)

. If the two lines intersect at the point

(a, b)

, what is the value of

a-b

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1

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-9

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-5

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0

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4

x y

A

is represented by the equation

(x-2)^{2}+(y+3)^{2}=1

B

is represented by the equation

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(x+2)^{2}+(y+5)^{2}=1

. Which of the following statements about the two circles is true?

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1

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B

2

units to the left of and

2

units below Circle

A

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B

2

units to the right of and

2

units above Circle

A

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B

4

units to the left of and

2

units below Circle

A

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B

4

units to the right of and

2

units above Circle

A

Write the equation of the parabola that passes through the points

(1,0)

(2,0)

(3,\text{–}16)

. Write your answer in the form

y = a(x – p)(x – q)

a

p

q

are integers, decimals, or simplified fractions.

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